Prison reformers have renewed a call for outsourcing companies G4S and Serco to be barred from bidding for any more government business until major fraud investigations into their criminal justice operations are completed.

The Howard League for Penal Reform published a dossier of incidents in which both companies have failed to deliver on their justice contracts over the past two years. It follows moves by ministers to allow the companies to resume bidding for government contracts after they agreed to repay £180m in total for overcharging the taxpayer on major electronic tagging contracts.

The dossier includes incidents in which specialist Macmillan cancer nurses were prevented, for contractual reasons, from entering a G4S-run prison to help a dying inmate. They also detail an incident in which a terminally-ill prisoner on his way to hospital was kept waiting on the street in handcuffs for 40 minutes while G4S staff went to a Greggs bakery for lunch.

It was published as an Ofsted inspection gave a G4S-run secure training centre a generally good report, but disclosed that the use of restraint had almost doubled since the previous inspection. At the Oakhill STC in Milton Keynes, for young offenders aged 12 to 18, 45% of young people told inspectors in February they had been restrained, compared with 23% when inspectors visited in 2013. The increase follows the introduction of a system of restraint that does not rely on inflicting pain.

Prison inspectors have also criticised the lack of rigour in the official response at a public sector high security prison where five prisoners have taken their own lives since they last visited in 2012.

The chief inspector of prisons, Nick Hardwick, said that there was a very high level of incidents of self-harm – almost double the normal level – at Woodhill prison at Milton Keynes.

He says that too many prisoners had felt victimised by staff and other prisoners: "Recorded levels of assaults on prisoners and staff were more than double that at other local prisons but the level of fights was similar. We were not, however, confident that all incidents had been adequately recorded," says the inspector's report, also published on Tuesday.

The inspectors say their verdict on Woodhill is mixed with some improvements in the prison's approach to safety over the last two years but the outcomes are still not good enough and very disappointing for some prisoners.

The chief inspector says that the amount of time that prisoners spent out of their cells had deteriorated considerably to only four to six hours a day for most inmates. He says there are too few purposeful activity places and a quarter of the population are unemployed.

Michael Spurr, the chief executive of the National Offender Management Service, which runs prisons and probation, said that Woodhill held some of the most difficult and disruptive prisoners in the system so he was glad to see the inspector recognised that improvements have been made in providing a safe and respectful environment.

"The governor and his staff are working hard to reduce incidents of violence and to improve rehabilitation – they will use the recommendations of this report to accelerate that work," said Spurr.